A new approach to exact cone-beam reconstruction without Radon transform

Abstract

Most exact cone-beam reconstruction methods are based on the Tuy-Smith-Grangeat formula which links cone-beam projections to the 3-D Radon transform. The computation of the 3-D Radon transform in these methods leads to drawbacks such as much computational requirements and significant discretization errors. The authors propose new exact cone-beam reconstruction method which does not explicitly compute the 3-D Radon transform. The new method is based on two familiar concepts in 3-D tomography fields which are the approximate ramp reconstruction (the cone-beam backprojection after the ramp filtering) and the Fourier synthesis based on the central slice theorem. Simulation results demonstrate that the new method requires less computational requirements and suffers from less discretization errors in typical cases.